3.17 \(\int \frac{1}{x^3} \, dx\)

Optimal. Leaf size=7 \[ -\frac{1}{2 x^2} \]

[Out]

-1/(2*x^2)

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Rubi [A]  time = 0.0004021, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {30} \[ -\frac{1}{2 x^2} \]

Antiderivative was successfully verified.

[In]

Int[x^(-3),x]

[Out]

-1/(2*x^2)

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin{align*} \int \frac{1}{x^3} \, dx &=-\frac{1}{2 x^2}\\ \end{align*}

Mathematica [A]  time = 0.0001609, size = 7, normalized size = 1. \[ -\frac{1}{2 x^2} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(-3),x]

[Out]

-1/(2*x^2)

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Maple [A]  time = 0., size = 6, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,{x}^{2}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^3,x)

[Out]

-1/2/x^2

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Maxima [A]  time = 0.97134, size = 7, normalized size = 1. \begin{align*} -\frac{1}{2 \, x^{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^3,x, algorithm="maxima")

[Out]

-1/2/x^2

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Fricas [A]  time = 1.45694, size = 14, normalized size = 2. \begin{align*} -\frac{1}{2 \, x^{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^3,x, algorithm="fricas")

[Out]

-1/2/x^2

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Sympy [A]  time = 0.051958, size = 7, normalized size = 1. \begin{align*} - \frac{1}{2 x^{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**3,x)

[Out]

-1/(2*x**2)

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Giac [A]  time = 1.089, size = 7, normalized size = 1. \begin{align*} -\frac{1}{2 \, x^{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^3,x, algorithm="giac")

[Out]

-1/2/x^2